Puzzle.



ment'of myinvention, and in Fig. 2 a similar form and dimensions, andtherefore suscep- UNITED STATES Patented May 19, 1903.

PATENT OFFICE. Y

BENJAMIN G. LAMME, OF PITTSBURG, PENNSYLVANIA.

, ".P-UZZLEQ SPECIFICATION forming part of Letters Patent No.vaazaauatea May 19, 1903.

Application filed June 25, 1901.

To all whom it may concern:

Be it known that I, BENJAMIN G. LAMME, a citizen of the United States,residing at Pittsburg, in the county of Allegheny and State ofPennsylvania, have invented a new and useful Improvementin Games orPuzzles, of which the following is a specification.

My invention relates to games or puzzles; and it has for its object toprovide an arithmetical game or puzzle theessential physical elements ofwhich are simpleand inexpensive and which are susceptible of manipula-'tion to bring them into a considerable nu mber of different relativearrangements, but being susceptible of one special arrangement whichaffords a solution of the game or puz: zle, and in which certainpeculiar and remarkable arithmetical combinations are presented. 7 1

In Figure 1 of the accompanying drawings I have illustrated in plan viewone embodiview of a modification.

The, elements of my invention are blocks which severally havefour unlikenumbers on at least one face and which'may be of any material and anythickness and surface dimensions, the blocks being all of the same tibleof many relative arrangements to form an invariable geometrical figure,but being susceptible of only one arrangement which constitutes asolution of the game or puzzle. In Fig. 1 I have shown sixteen blocks,each of which is divided by two lines perpendicular to each other intofour equal squares, the whole number of small squares being thereforesixty-four, each of which is provided with a different number, thenumbers being from 1 to 64:,finclusive, and none being used more thanonce. I The numbers on each block are such that their sum equals onehundred and thirty, and they are so arranged that there is a differenceof one between two of the diagonally-disposed numbers and a differenceof three between the other two diagonally-disposed numbers on eachblock. The entire number of blocks when arranged in the form of a squaremay be designated as the primary squ are,and this is composed of foursecondary squares, each of which contains four blocks. When thusarranged in am... 66.147. (Ilo moaei.

a complete square, there are eight horizontal and eight vertical linesof eight numbers reach and two full diagonals of eight numberseach. Thepartial diagonals on each side of the main diagonals obviously vary fromseven numbers to one, and each two with this combination of blockshaving the I face'numbers thereon, as above described, is

to so arrange the sixteen blocks as to present certain peculiararithmetical combinations andresults as follows: When the blocks are 4..

properly arranged, the sum of each four numbers in a horizontal line onany two adjacent blocks is one hundred and thirty", and consequently thesum of the numbers in each horizontal line across the primary squareamounts to two hundred and sixty. The sum of the four numbers in eachvertical line on any two adjacent blocks is one hundred and thirty andtherefore, the sum of the numbers in each vertical line of the primarysquare is two hundred and sixty. The sum of the four numbers on eachblockis'one'hundred and thirty and also the sum of each four numbersconstituting a square,whether these numbers be on one, two, or fourdifferent blocks, is one hundred and thirty. For example:

The sum of the numbers in eachof the main diagonals of the primarysquare is two hun- ;dred and sixty and the sum of the numbers in each,two complementary diagonals is also two hundred and sixty. Consideringnow the secondary squares which severally com prise four blocks, we findthatthe sum of the numbers in each of the two main diagonals is onehundred and thirty and the sum of. the four numbers in any twocomplementary diagonals is one hundred and thirty. These conditions aretrue with reference to each of the four secondary squares. The sum. ofthe alternate numbers in each full diagonal and in each twocomplementary diagonals of each secondary square is sixty-five-i. 6.,one-half dred and ninety.

the sum of all the numbersin each full diagonal, each two complementarydiagonals, each four numbers constituting a square, each vertical lineof four numbers, and each horizontal line of four numbers.

In Fig. 2 I have shown a primary square composed of thirty-six blocks,each of which is divided into four squares, the same as the blocks shownin Fig. 1, the entire set of numbers on the primary square being fromone to one hundred and forty-four, inclusive. The combination andarrangementofnumbers are the same as in the square shown in Fig. 1 andalready described, except that the sum of the numbers on each block istwo hundred and ninety and the sum of each four numbers forminga square,whether on the same block, on two blocks, or on four blocks, is twohundred and ninety. Also the sum of each horizontal line of numbers onany two adjacent blocks is two hundred and ninety and the sum of eachvertical line of four numbers on any two adjacent blocks is two hundredand ninety. In this form there are nine secondary squares of four blockseach, and the sum of the numbers in each main diagonal, as well as ineach two complementary diagonals in each of these secondary squares, istwo hun- The sum of the numbers in each diagonal of the primary squareand in each two complementary diagonals of the primarysquareiseighthundred and seventyz'. 6., three times the corresponding sums onthe secondary squares. In this embodiment of my invention the sum ofalternate numbers in each full diagonal and in each two complementarydiagonals of each secondary square is one hundred and forty-five7l. 6.,one-half the sum of each combination of numbers above described aspertaining to the secondary squares.

In each embodiment of my invention the difference between two of thediagonally-disposed numbers on each block is equal to the lowest numberof the entire set, andthe difference between the other two diagonals oneach block is equal to three times the lowest number of the entire'set.

While I have shown the invention as embodied in one set of sixteenblocks and inone of thirty six blocks, it will be understood that theinvention is susceptible of further variation as regards the number ofblocks and also as regards the numerals employed, and it is therefore myintention to cover and include the employment of any number of blockssusceptible of arrangement into squares in the same general manner asthat specifically disclosed, it being understood that there will be fournumbers on each block, that no number will be used twice, and thataproper arrangement of the blocks will insure such relative location oftheir numbers as will provide the combinations set forth in the claims.

Instead of employing a set of numbers that are consecutive from thelowest to the highest the several numbers in the set may be the productswhich result from multiplying consecutive numbers by any constant, inwhich case the constant obtained by adding together certain horizontal,vertical, and diagonal lines of numbers and certain numbers constitutingsquares will equal the product secured by multiplying the sumshereinbefore given by the constant used as a multiplier of theconsecutive numbers. For example, if the numbers shown in Fig. 1 are allmultiplied by five the sum of eachline of four numbers on adjacentblocks and of each four numbers forming a square will be six hundred andfifty'. a, five times one hundred and thirty. In general it will beobserved that the constant which is employed as a m ultiplier of theconsecutive numbers appears as a factor in the results secured bycombining the products in the manner hereinbefore set forth.

I have illustrated blocks having square faces and have designatedcertain combinations of individual blocks and certain combinations ofthe surface numbers as constituting squares without any intention ofnecessarily limiting the shape of either the individual blocks, theprimary and secondary combinations of such blocks, or the arrangement ofthe surface numbers to what would be signified by a strict geometricaluse of the term square. It will be understood that the faces of theblocks may have any one of a large number of difierent shapes and thatthe numbers may have quadrangular arrangements on the block-faces whichwould aiford the results hereinbefore set forth, or at least some ofthem, even though the figures thus outlined by the numbers were neithersquares nor rectangles. The terms vertical and horizontal are also notused in a strict geometrical sense, since an arrangement of the numberson the faces of the blocks so that they may be arranged in approximatelystraight lines that intersect each other otherwise than at right anglesis within the scope of my invention.

Whatever may be the shape of the individual blocksit is obvionsthat thenumbers may be so disposed thereon that when the blocks are assembledthe numbers will form two sets of parallel lins which intersect eachother, and the sum of each four numbers in alinement on adjacent blocksin each of such sets is a constant. If the numbers are not uniformlydisposed in squares, there will of course be no straight-line diagonalsthe sum of the numbers of which will have the characteristicshereinbefore set forth.

I claim as my invention- 1. A plurality of blocks each of which has fournumbers in its respective corners and all of said blocks being adaptedto form a square on which the sum of each four numbers constituting asquare is constant.

2. A plurality of blocks which are respectively provided with fournumbers in their corners and which collectively have unlike numbers,said blocks being adapted to 'form a square on which the sum of eachfour numbersconstituting a square is'cons'tant.

3. A plurality of blocks which are respectively provided with fournumbers intheir corners and which collectively have unlike numbers, saidblocks being adapted to form a square on which the sum of each fournumbers constituting a square is equalto the sum of each vertical lineof four numbers on any two adjacent blocks. 7

4. A plurality of blocks which are respectively provided with fournumbers in their numbers, said blocks being adapted to form a square onwhich the sum of each horizontal line of four numbers on any twoadjacent blocks is equal to the sum of each vertical line of fournumbers on any two adjacent blocks and is also equal to the sum of anyfour numbers constituting a square, whether on one, two or four blocks.

6. A plurality of blocks which are respec tively provided with fournumbers in their corners and which collectively have unlike numbers,said blocks being adapted to form a square on which the sum of each fulldiagonal line of numbers is equal to the sum of each two complementarydiagonal lines of numbers.

7; A plurality of blocks which are respectively provided with fournumbers in their corners and which collectively have unlike numbers,said blocks being adapted to form a primary square consisting of aplurality of secondary squares 'the sum of the numbers in each fulldiagonal line of each of which is equal to the sum of the numbers ineach two complementary diagonal lines.

8. A plurality of blocks which are respectively provided with numbers intheir corners and which collectively have unlike numbers, said blocksbeing adapted to form a primary square composed of a plurality ofsecondary squares upon which the numbers are so arranged that the sum ofeach full diagonal line of numbers is equal to the sum of each twocomplementary diagonal lines; to the sum of each horizontal line of fournumbers and to the sum of each vertical line of four numbers and to thesum of each four numbers constituting a square on any part of theprimary square.

9. A plurality of blocks which are respectively provided withfour'numbers in their corners and which collectively have-unlikenumbers, said blocks being adapted to form a primary square comprising aplurality of secondary squares of four blocks each, in

which the sum of the alternate numbers in v each full diagonal and ineach twocomple mentary diagonals isequal to one-half the offour numberson each ofsaid secondary squares and to one-half of the sum of any fournu mbers constituting a square anywhere onthe primary square. l

10. A plurality of blocks which are respectively provided with fournumbers in their corners and which are collectively provided withconsecutive numbers, the difference between two of thediagonally-disposed .numbers on each block being'one and the d-iiferencebetween the other two diagonally disposed numbers on each block beingthree.

11. A plurality of blocks which are respectively provided with fournumbers intheir corners and which are collectively provided with unlikenumbers so selected and arranged that the difference between two of thediagonally-disposed numbers on the several blocks is a constant for theentire set and the difierence between the other two diagonally-disposednumbers on the several blocks is a dif-- ferentconstant for the entireset.

12. A plurality of blocks which are respectively provided with numbersin their corners and which collectively have consecutive numbers, saidblocks being adapted to form a square composed of a plurality ofsecondary squares of four blocks each upon which the numbers are soarranged thataconstant quantity results from adding each of thefollowing 7 I j with unlike numbers so selected and arranged that thedifference between two of the diagonally-disposed numbers on the severalblocks is equal to the lowest number ofthe entire set and the difierencebetween the other two.

diagonally-disposed numbers on the several ber of the entire set.

14. A set of blocks which are severally provided with foursymmetrically-disposed numbers, which collectively have unlike numbersand which. are adapted to form a geometrical figure on which the sum ofeach four 'numbe'rs forming a quadrangle is constant.

15. A set of blocks which are severally pro vided with foursymmetrically-disposed numbers, which collectively have unlike numbersand which are adapted to form'a geometrical figure comprising aplurality of secondary figary figures being constant.

16. A set of blocks which are severally pro- I I 5 blocks is equal tothree times the lowest numures of four blocks each, the sum of each fournumbers in alinement on-each of the secondvided with foursymmetrically-disposed'numw bers, which collectively have unlike numbersand which are adapted to form a geometrical figure on which the sum ofeach four num bers in alinement, and not diagonal, on adjacent blocksequals the sum of each four numbers constituting a quadrangle.

17. A set of blocks which are severally provided with foursymmetrically-disposed numbers, which collectively have unlike numbersand which are adapted to form a geometrical figure comprising aplurality of secondary figures of four blocks each, the sum of each fournumbers in alinement on each of the secondary figures being equal to thesum of each four numbers constituting a quadrangle on any part of theprimary square.

18. A set of blocks bearing a series of unlike numbers, each of saidblocks having four of four numbers constituting a square a e,

where on the primary figure.

In testimony whereof I have hereunto sub scribed my name this 25th dayof June, 1901.

, BENJ. G. LAMME. Witnesses:

JAMES B. YOUNG, WESLEY G. CARR.

